Taller de Regla Falsa y Bisección

Solución taller de la regula falsi y bisección f($) % $10 & 1 BISECCION

Iteración 1 2 3 " 5 6 !

Xinferior (Xl) 0 0.65 0.!5 0.!5 0.!5 0.!5 0.532

Xsuperior (Xu) 1.3 1.3 1.3 1.13!5 1.05625 1.01563 1.01563

Xr   0.65 0.!5 1.13!5 1.05625 1.015625 0.5315 1.005"!5

REGULA FALSI

Iteración 1 2 3 " 5 6 ! #  10 11 12 13 1" 15

Xinferior (Xl) 0 0.0"3 0.1#1!6 0.262## 0.33#11 0."0!## 0."!25 0.5325# 0.5##15 0.6355 0.6#65 0.!30"5 0.!!01 0.#051 0.#3!##

Xsuperior (Xu) 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3

Xr   0.0"26 0.1#1!52 0.262#!51 0.33#110! 0."0!##25 0."!25#51 0.5325!! 0.5##152" 0.635" 0.6#6"#! 0.!30"52! 0.!!0102 0.#050#6 0.#3!#!61 0.#66033

16 1! 1# 1 20

0.#6603 0.#056 0.11"2 0.2#6 0."35

1.3 1.3 1.3 1.3 1.3

0.#0"53 0.11"153 0.2#612 0."3"# 0.553#5

Inter'alo 0 1.3* +pai 33.333333333 1".2#5!1"2#6 !.6230!623 " 2.0"0560023! 1.010"6!6#"

+pai "#.11#"05!"5 30.#5!1!25" 22.251!6!#1# 1!.105#5#11 13.612123"! 11.26"6010"3 .""00#"112 #.0363!561" 6.0003#!!1" 5.55!551306 5.1"#5!65236 ".""301!05!6 3.#152!2601 3.2512"!0#"1

Xe$acto

1

,(Xr)

,(XI)

-0.9865373 -0.2236704 2.62672022 0.72849139 0.16770685 -0.0458745 0.05611879

-1 -0.98654 -0.22367 -0.22367 -0.22367 -0.22367 -0.04583

,(Xu)

,(Xr)

,(XI)

12.!#5#"1#5

-1 -1 -0.9999984 -0.9999805 -0.9998725 -0.9994444 -0.9981642 -0.9950467 -0.9885518 -0.9765985 -0.9567565 -0.9266361 -0.8844265 -0.8294711 -0.7626746

-1 -1 -1 -1 -1 -0.99987 -0.99944 -0.99816 -0.99505 -0.98855 -0.9766 -0.95676 -0.92664 -0.88442 -0.82946

+pa 35 2.5 13.!5 5.625 1.5625 0."6#5 0.5"!5

+pa 0.5!00" #1.#2"0!5 !3.!12"" 66.1##3" 5.211!5" 52.!"1"1 "6.!"221" "1.1#"!5! 36.0"5101 31.30512# 26.5"!31 22.##02 1."0136 16.2123 13.36!03

12.!#5#"1#5 12.!#5#"1#5 12.!#5#"1#5 12.!#5#"1#5 12.!#5#"1#5 12.!#5#"1#5 12.!#5#"1#5 12.!#5#"1#5 12.!#5#"1#5 12.!#5#"1#5 12.!#5#"1#5 12.!#5#"1#5 12.!#5#"1#5 12.!#5#"1#5

2.!"311!!"15 2.22!13"" 1.###!!03"#3 1.5"0!333!0# 1.2""3013"

10.5"06# #.#5#"6# !.103#!5" 5.650165 "."61"0!

12.!#5#"1#5 12.!#5#"1#5 12.!#5#"1#5 12.!#5#"1#5 12.!#5#"1#5

-0.6865698 -0.6044848 -0.5213964 -0.4410023 -0.3664391

-0.76268 -0.68622 -0.60446 -0.5214 -0.44099

Paso 3 : Ra!"#a$ !as s"%&"'(s )a!&a*"o's +a$a ,(

a S" "'$  0 '(o'*s !a $a"# s

/ S" ;"'$ < 0 '(o'*s !a $a"# s * S" "'$  0 !a $a"# s "%&a! a 

,(Xl)-,(Xr)

0.98653726 0.22065916 -0.58751951 -0.16294194 -0.03751105 0.01026077 -0.00257173

,(Xl)-,(Xr)

1 0.99999996 0.99999838 0.9999789 0.99985302 0.99931698 0.99760949 0.99321985 0.98365534 0.96541803 0.93436656 0.88656658 0.81954323 0.73360462 0.63261045

0.52363492 0.4148067 0.31516557 0.22993985 0.16159623

$"'a$ ' & s&/"'($)a!o s( !a $a"#:

'*&'($a ,'($o ,! s&/"'($)a!o "'$"o$ o "#&"$,o. Po$ (a'(o s a* s&+

'*&'($a ,'($o ,! s&/"'($)a!o s&+$"o$ o ,$*o. Po$ (a'(o s a* "'  $  ($"'a ! +$o*so , *!*&!o

$  )o!)$ a! +aso 2

$  )o!)$ a! +aso 2